ODE
\[ x^3 y'''(x)-3 x^2 y''(x)+7 x y'(x)-8 y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0102482 (sec), leaf count = 24
\[\left \{\left \{y(x)\to x^2 \left (c_3 \log ^2(x)+c_2 \log (x)+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) ={x}^{2} \left ( \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C3}+{\it \_C2}\,\ln \left ( x \right ) +{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[-8*y[x] + 7*x*y'[x] - 3*x^2*y''[x] + x^3*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^2*(C[1] + C[2]*Log[x] + C[3]*Log[x]^2)}}
Maple raw input
dsolve(x^3*diff(diff(diff(y(x),x),x),x)-3*x^2*diff(diff(y(x),x),x)+7*x*diff(y(x),x)-8*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x^2*(ln(x)^2*_C3+_C2*ln(x)+_C1)